Functions and Function Notations

Front

What is a function?

Back

A function is a relation where every input (x-value) has exactly one output (y-value).

Front

Given the function f(x) = 2x + 3, what is f(1)?

Back

f(1) = 2(1) + 3 = 5.

Front

What is the notation for a function?

Back

The notation for a function is typically f(x), where 'f' is the function name and 'x' is the input variable.

Front

Is the relation {(1,2), (2,3), (1,4)} a function?

Back

No, it is not a function because the input '1' has two different outputs (2 and 4).

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

Given f(x) = -x + 4, find f(2).

Back

f(2) = -2 + 4 = 2.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Given f(x) = 3x - 5, find x when f(x) = 4.

Back

3x - 5 = 4; 3x = 9; x = 3.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, it is not a function.